The present general inventive concept is directed toward adaptive spatial resolution of mesh nodes in simulating electric circuits during the design phase thereof. The present general inventive concept finds application in simulating the electrical behavior of split plane electrical circuits through a mesh of linked nodes, the spatial resolution of which is adapted in accordance with the shape of the planes forming the electrical circuit.
Split plane power distribution is a common circuit configuration to distribute electrical power to functional components of a broader electrical circuit design. As illustrated in FIG. 1A, split plane power distribution is generally implemented by a power plane 110 and a ground plane 120, the combination of which will be referred to herein as a power/ground plane pair (PGPP) 100. Typically, the power plane 110 and the ground plane 120 are spaced apart in planar parallel alignment, and are separated by a dielectric medium.
Typically, split-plane power distribution networks must accommodate extremely rapid switching times of current across its domain. As these switching times are ever increasing from one generation of circuits to another, power integrity (PI) analysis has become a focus of circuit designers, whereby the power distribution network can be simulated and modified in the design phase. Due to the geometry of the PGPP and the switching times involved, transmission line modeling is typically employed to analyze the frequency dependent characteristics of the PGPP during the design stage so that prudent design measures can be taken. For example, as illustrated in FIG. 1B, a PGPP model 130 includes a plurality of transmission line segment models 140 each contained within a cell 135. When the PGPP model 130 is executed, a frequency response of the PGPP can be analyzed. Accordingly, when resonance is apparent in the impedance profile at some frequency, for example, the designer may add capacitive elements at certain points in the PGPP to favorably alter the resonant frequency components of the power distribution network. Since, through PI analysis, such modification can be achieved at the design phase and prior to the fabrication of an actual circuit, the time to market of a product using the circuit can be decreased considerably.
Whereas, it is not difficult to model a simple plane pair transmission line, the abstract shapes of typical PGPPs result in complex boundaries some of which may be internal to the exterior boundary of the PGPP. For example, as illustrated in FIG. 1B, many PGPP models, such as PGPP model 130, are implemented in a uniform mesh of cells 135 so that complex shapes can be accommodated. Consequently, an extremely large number of cells 135 may be needed to populate the entirety of the PGPP model 130. While several algorithms can be used to model the complex shapes of a PGPP, the computational overhead for these algorithms are prohibitive, especially where such PI analysis tools must share computational resources with other design tools.